To divide the fractions [tex]\(\frac{3}{16}\)[/tex] and [tex]\(\frac{15}{2}\)[/tex], we can follow these steps:
1. Understand the Operation: Division of fractions is equivalent to multiplying the first fraction by the reciprocal of the second fraction. Therefore,
[tex]\[
\frac{3}{16} \div \frac{15}{2} = \frac{3}{16} \times \frac{2}{15}
\][/tex]
2. Multiply the Numerators:
Multiply the numerators of the two fractions:
[tex]\[
3 \times 2 = 6
\][/tex]
3. Multiply the Denominators:
Multiply the denominators of the two fractions:
[tex]\[
16 \times 15 = 240
\][/tex]
4. Form the New Fraction:
Now we have:
[tex]\[
\frac{3}{16} \times \frac{2}{15} = \frac{6}{240}
\][/tex]
5. Simplify the Fraction:
Find the greatest common divisor (GCD) of 6 and 240 to simplify the fraction to its lowest terms. The GCD of 6 and 240 is 6. Simplify by dividing both the numerator and the denominator by their GCD:
[tex]\[
\frac{6 \div 6}{240 \div 6} = \frac{1}{40}
\][/tex]
Therefore, the answer is:
[tex]\[
\frac{3}{16} \div \frac{15}{2} = \frac{1}{40}
\][/tex]
